Hawaiian Airlines pilots said “a large gap” still remains in labor negotiations with the company.

The Air Line Pilots Association, which began talks with the company nearly 16 months ago, said Thursday it wants the National Mediation Board to establish a hard deadline to reach an agreement.

Both the pilots union and the company met with the mediation board at the beginning of the month in a status conference and then proceeded to engage in three days of negotiations. The two sides have had more than 30 mediation sessions without reaching an agreement.

“During our status conference we presented to the NMB the reasons we believe that negotiations should conclude soon with an industry appropriate agreement, and the need for the NMB to establish a deadline in the case,” Hawaiian Airlines Capt. Hoon Lee, chairman of Hawaiian’s Master Executive Council, said Thursday in an email. “We believe that the facts, circumstances and reasons we presented were compelling. We followed our presentation with three days of mediation during which we continued to make new proposals and demonstrate Hawaiian pilots’ willingness to be flexible and achieve a new contract. We’re hopeful that, after its internal deliberations, the NMB will agree that it’s time for the parties to conclude negotiations and that it will take steps within its authority to make that happen in the near future.”

If no agreement is reached and the two sides are released from mediation, the union and the company would proceed to the next step, which would be arbitration by an independent party where the decision would be binding. If either side rejects going to arbitration, a 30-day cooling-off period would ensue after which a strike by the pilots could occur.

The company said it is focused on reaching a contract with the pilots.

”We are making progress and remain committed to reaching a market-based contract with the Air Line Pilots Association — a contract that offers our pilots wages, benefits and work rules that are in line with our competitive position in the industry,” Hawaiian spokesman Alex Da Silva said.

ALPA said in a recent memo to its pilots that during the latest mediation sessions the union made a proposal with modest adjustments in a few areas. ALPA said the company made a counterproposal that improved Airbus A330 aircraft pay rates and added money to the post-Medicare retiree health accounts that management has proposed to replace the pilots’ current post-Medicare health benefits.

“Unfortunately, the company pay rates proposed were only for the A330 and not other aircraft, and they lagged other comparable carriers both at the start and, by even larger amounts, at the end of the contract,” ALPA said. “Moreover, the company failed to address key priorities for Hawaiian pilots related to the elimination of pro-ration; our proposed increased value for training and vacation days; implementation of a minimum flight grouping credit; and, retroactive pay for the company’s delay finishing these negotiations, among other things.”

Hawaiian’s stock closed Thursday up 48 cents at $45.12. The shares have increased 27.7 percent since the beginning of the year.